File photo of an Air New Zealand Boeing 787-9 (ZK-NZE). Image courtesy of Masakatsu Ukon.
Update: British Airways has started cutting their 787 flights as well, due to the same reason as the ANZ 787s (fan blade corrosion on the Rolls-Royce Trent 1000 engine). Stay tuned for more info. Source: https://thepointsguy.com/2017/12/british-airways-is-canceling-a-lot-of-flights-because-of-787-engine-trouble/
Update (December 12, 2017): Air New Zealand will be leasing an Airbus A330 and an Airbus A340 from Portuguese wet-lease specialist Hi Fly to cover the capacity lost by the grounded 787s, according to FlightGlobal. Source: https://www.flightglobal.com/news/articles/air-nz-wet-leases-hi-fly-aircraft-to-cover-787-maint-444043/
On December 7, Air New Zealand officially announced the scaling-back of its Boeing 787 operations, due to problems with the Rolls-Royce Trent 1000 engines that power the aircraft. According to BBC, just this past week, two 787s returned to Auckland after engine problems were reported mid-flight, requiring Air New Zealand to conduct maintenance checks on the affected aircraft.
Air New Zealand has, in a statement, said that the 787-9's Rolls-Royce engines require "maintenance sooner than previously advised."
Because of the aforementioned engines issues, Air New Zealand will "cancel and delay flights each day over the coming weeks." The two engine incidents this week, on flights to Tokyo, Japan and Argentina, are currently being investigated by the New Zealand Transport Investigation Commission. Furthermore, the New Zealand Herald reported that passengers on the flight to Tokyo, Japan experienced shaking and heard "weird noises."
Over the past year, Japan's ANA and Great Britain's Virgin Atlantic both reported problems with the Rolls-Royce Trent 1000 engine that power their 787 Dreamliner fleets. In August of this year, Rolls-Royce said that "components on some Trent 1000 engines were wearing out earlier than expected," according to BBC's reports. BBC also reported that Rolls-Royce is currently working with Air New Zealand on pinpointing the cause of the 787's engine troubles, saying that it's "not uncommon for long-term engine programs to experience technical issues during their life."